MULTIPLICATIVE PRIMENESS OF COMPLEXIFICATION FOR REAL ALGEBRAS

We say that an algebra a is multiplicative prime if both a and m(a) ( the multiplication algebra of a) are prime . in this paper , we study the transitivity of the property of multiplicative primeness for real normal algebra when one take the process of the complexification of such real algebra . we prove that if a is a real normal multiplication of a is also multiplicatively prime normed algebra .